In view of their capabilities, generative models have recently been considered as priors in a Bayesian treatment of inverse problems, cf., e.g., [1]}.
The advantage of such proceeding is that individual properties of the problem at hand, such as the structure of brain images, are adequately taken into account [2]}, which leads to an improved inference. Another advantage is that often the sought (discrete) function or field belongs to a low-dimensional manifold, which is exploited by current generative models such as GANs or VAEs. Then, the inference can be carried out in a low-dimensional space of latent variables, which strongly facilitates the calculation of the results in a Bayesian inference, cf. [3]}, [4]}, [5]}, [6]}.
